added option show_mode_inference; added splitting of conjunctions in expand_tuples
(* Author: Lukas Bulwahn, TU Muenchen
Auxilary functions for predicate compiler
*)
structure Predicate_Compile_Aux =
struct
(* general syntactic functions *)
(*Like dest_conj, but flattens conjunctions however nested*)
fun conjuncts_aux (Const ("op &", _) $ t $ t') conjs = conjuncts_aux t (conjuncts_aux t' conjs)
| conjuncts_aux t conjs = t::conjs;
fun conjuncts t = conjuncts_aux t [];
(* syntactic functions *)
fun is_equationlike_term (Const ("==", _) $ _ $ _) = true
| is_equationlike_term (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ _)) = true
| is_equationlike_term _ = false
val is_equationlike = is_equationlike_term o prop_of
fun is_pred_equation_term (Const ("==", _) $ u $ v) =
(fastype_of u = @{typ bool}) andalso (fastype_of v = @{typ bool})
| is_pred_equation_term _ = false
val is_pred_equation = is_pred_equation_term o prop_of
fun is_intro_term constname t =
case fst (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl t))) of
Const (c, _) => c = constname
| _ => false
fun is_intro constname t = is_intro_term constname (prop_of t)
fun is_pred thy constname =
let
val T = (Sign.the_const_type thy constname)
in body_type T = @{typ "bool"} end;
fun is_predT (T as Type("fun", [_, _])) = (snd (strip_type T) = HOLogic.boolT)
| is_predT _ = false
(*** check if a term contains only constructor functions ***)
fun is_constrt thy =
let
val cnstrs = flat (maps
(map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
(Symtab.dest (Datatype.get_all thy)));
fun check t = (case strip_comb t of
(Free _, []) => true
| (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of
(SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname' andalso forall check ts
| _ => false)
| _ => false)
in check end;
fun strip_ex (Const ("Ex", _) $ Abs (x, T, t)) =
let
val (xTs, t') = strip_ex t
in
((x, T) :: xTs, t')
end
| strip_ex t = ([], t)
fun focus_ex t nctxt =
let
val ((xs, Ts), t') = apfst split_list (strip_ex t)
val (xs', nctxt') = Name.variants xs nctxt;
val ps' = xs' ~~ Ts;
val vs = map Free ps';
val t'' = Term.subst_bounds (rev vs, t');
in ((ps', t''), nctxt') end;
(* introduction rule combinators *)
(* combinators to apply a function to all literals of an introduction rules *)
fun map_atoms f intro =
let
val (literals, head) = Logic.strip_horn intro
fun appl t = (case t of
(@{term "Not"} $ t') => HOLogic.mk_not (f t')
| _ => f t)
in
Logic.list_implies
(map (HOLogic.mk_Trueprop o appl o HOLogic.dest_Trueprop) literals, head)
end
fun fold_atoms f intro s =
let
val (literals, head) = Logic.strip_horn intro
fun appl t s = (case t of
(@{term "Not"} $ t') => f t' s
| _ => f t s)
in fold appl (map HOLogic.dest_Trueprop literals) s end
fun fold_map_atoms f intro s =
let
val (literals, head) = Logic.strip_horn intro
fun appl t s = (case t of
(@{term "Not"} $ t') => apfst HOLogic.mk_not (f t' s)
| _ => f t s)
val (literals', s') = fold_map appl (map HOLogic.dest_Trueprop literals) s
in
(Logic.list_implies (map HOLogic.mk_Trueprop literals', head), s')
end;
fun maps_premises f intro =
let
val (premises, head) = Logic.strip_horn intro
in
Logic.list_implies (maps f premises, head)
end
(* lifting term operations to theorems *)
fun map_term thy f th =
setmp quick_and_dirty true (SkipProof.make_thm thy) (f (prop_of th))
(*
fun equals_conv lhs_cv rhs_cv ct =
case Thm.term_of ct of
Const ("==", _) $ _ $ _ => Conv.arg_conv cv ct
| _ => error "equals_conv"
*)
(* Different options for compiler *)
datatype options = Options of {
(*check_modes : (string * int list list) list,*)
show_steps : bool,
show_mode_inference : bool,
show_proof_trace : bool,
show_intermediate_results : bool,
(*
inductify_functions : bool,
*)
inductify : bool,
rpred : bool
};
fun show_steps (Options opt) = #show_steps opt
fun show_mode_inference (Options opt) = #show_mode_inference opt
fun show_intermediate_results (Options opt) = #show_intermediate_results opt
fun show_proof_trace (Options opt) = #show_proof_trace opt
fun is_inductify (Options opt) = #inductify opt
fun is_rpred (Options opt) = #rpred opt
val default_options = Options {
show_steps = false,
show_intermediate_results = false,
show_proof_trace = false,
show_mode_inference = false,
inductify = false,
rpred = false
}
fun print_step options s =
if show_steps options then tracing s else ()
(* tuple processing *)
fun expand_tuples thy intro =
let
fun rewrite_args [] (pats, intro_t, ctxt) = (pats, intro_t, ctxt)
| rewrite_args (arg::args) (pats, intro_t, ctxt) =
(case HOLogic.strip_tupleT (fastype_of arg) of
(Ts as _ :: _ :: _) =>
let
fun rewrite_arg' (Const ("Pair", _) $ _ $ t2, Type ("*", [_, T2]))
(args, (pats, intro_t, ctxt)) = rewrite_arg' (t2, T2) (args, (pats, intro_t, ctxt))
| rewrite_arg' (t, Type ("*", [T1, T2])) (args, (pats, intro_t, ctxt)) =
let
val ([x, y], ctxt') = Variable.variant_fixes ["x", "y"] ctxt
val pat = (t, HOLogic.mk_prod (Free (x, T1), Free (y, T2)))
val intro_t' = Pattern.rewrite_term thy [pat] [] intro_t
val args' = map (Pattern.rewrite_term thy [pat] []) args
in
rewrite_arg' (Free (y, T2), T2) (args', (pat::pats, intro_t', ctxt'))
end
| rewrite_arg' _ (args, (pats, intro_t, ctxt)) = (args, (pats, intro_t, ctxt))
val (args', (pats, intro_t', ctxt')) = rewrite_arg' (arg, fastype_of arg)
(args, (pats, intro_t, ctxt))
in
rewrite_args args' (pats, intro_t', ctxt')
end
| _ => rewrite_args args (pats, intro_t, ctxt))
fun rewrite_prem atom =
let
val (_, args) = strip_comb atom
in rewrite_args args end
val ctxt = ProofContext.init thy
val (((T_insts, t_insts), [intro']), ctxt1) = Variable.import false [intro] ctxt
val intro_t = prop_of intro'
val concl = Logic.strip_imp_concl intro_t
val (p, args) = strip_comb (HOLogic.dest_Trueprop concl)
val (pats', intro_t', ctxt2) = rewrite_args args ([], intro_t, ctxt1)
val (pats', intro_t', ctxt3) =
fold_atoms rewrite_prem intro_t' (pats', intro_t', ctxt2)
fun rewrite_pat (ct1, ct2) =
(ct1, cterm_of thy (Pattern.rewrite_term thy pats' [] (term_of ct2)))
val t_insts' = map rewrite_pat t_insts
val intro'' = Thm.instantiate (T_insts, t_insts') intro
val [intro'''] = Variable.export ctxt3 ctxt [intro'']
val intro'''' = Simplifier.full_simplify
(HOL_basic_ss addsimps [@{thm fst_conv}, @{thm snd_conv}, @{thm Pair_eq}])
intro'''
(* splitting conjunctions introduced by Pair_eq*)
fun split_conj prem =
map HOLogic.mk_Trueprop (conjuncts (HOLogic.dest_Trueprop prem))
val intro''''' = map_term thy (maps_premises split_conj) intro''''
in
intro'''''
end
end;